Whats the vertex of a parabola?
Round to the nearest hundredth.

To get the x-intercept we need the equation of the parabola;

the vertex form of the equation is given by:

y=a(x-h)^2+k

where:

(2,13) is the vertex:

Therefore;

y=a(x-2)^2+13

when x=0, y=5

Therefore the value of a will be:

5=a(0-2)^2+13

5-13=4a

4a=-8

a=-2

therefore the equation of the parabola will be:

y=-2(x-2)^2+13

y=-2x^2+8x+5

the x-intercept will be:

x=2-sqrt(7.5)

or

x=2+sqrt(7.5)

Step-by-step explanation:

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.